Influence of non linear geometrical parameter on curved thin shell buckling behaviour

The present paper deals with instabilities of long homogeneous and isotropic thin shells, characterized by geometrical nonlinearities and imperfections. It is therefore of interest for the designer to know how these structural elements behave under different loading conditions (lateral and/or hydrostatic pressure) especially with reference to a bent helicoidally geometrical shape of particular interest for the helicoidally Steam Generators tube bundle. Apparently no data exist in the literature to describe the non-linear buckling behaviour of curved thin shells under external pressure, thus the theoretical analyses, based on the classical linear elastic theory, and might be inadequate to evaluate the collapse load especially if the curvature is rather large. To the purpose of determining the buckling pressure load the effects of a pre-existing level of geometrical and technological imperfection, unavoidably caused by various manufacturing processes were also considered. A numerical analysis with available computing resources (FEM code) has allowed to take into account the nonlinear geometrical and material properties and to set up appropriate models to describe the buckling phenomenon. Moreover at Pisa University a rather intense experimental research activity is being carried out on the buckling of thin walled tube specimens in the dimensional range suitable for the above mentioned applications. A validation of numerical evaluations by comparison with test results is performed and the local character of buckling in the circumferential direction is also demonstrated as well as the relationship of the buckling stress on the severity of the initial defects (mainly diameter to thickness or tube/bending diameters ratios) on the collapse loads. A detailed knowledge of this dependency would lead to a better prediction of the buckling stress of the considered thin shell.